Question

What’s the inverse equation? And how you solved it step by step please!

Answer 1

Explanation:

There's a lot behind inverses regarding their graphs and whether the function is one-to-one, etc. But for our intents and purposes, we'll stick to the absolute basics and find the inverse without all the background stuff, ok?

The rule for finding an inverse algebraically is the first switch the x and y in the function, then solve for the new y.

Switching x and y (keep in mind that q(x) is the same thing as y):

`x=4+\sqrt[3]{y}`

To solve for the new y, we need to move the 4 over by subtraction first:

`x-4=\sqrt[3]{y}`

To get that y out from under the cubed root, we do the opposite of a cubed root which is to cube. So cubing both sides gives us:

`(x-4)^3=(\sqrt[3]{y})^3`

Of course cubing a cubed root is an inverse all its own, leaving us with just plain old y on the right:

`(x-4)^3=y`

That's the inverse. If you need it multiplied out, FOIL (x-4) together 3 times. But this might suffice because it is, after all, a valid way to state a function's inverse. Also, if you need that in inverse function notation, then this is the way you'd write that:

`q^(-1)(x)=(x-4)^3`